Computer Assisted Proof for Apwenian Sequences

An infinite ±1-sequence is called Apwenian if its Hankel determinant of order n divided by 2n-1 is an odd number for every positive integer n. In 1998, Allouche, Peyriere, Wen and Wen discovered and proved that the Thue--Morse sequence is an Apwenian sequence by direct determinant manipulations. Recently, Bugeaud and Han re-proved the latter result by means of an appropriate combinatorial method. By significantly improving the combinatorial method, we find several new Apwenian sequences with Computer Assistance. This research has application in Number Theory to determining the irrationality exponents of some transcendental numbers.